a boy pulls his toy on a smooth horizontal surface with a rope inclined at 60° to the horizontal if the effective Force pulling the toy along the horizontal surface is 5-newton calculate the tension in the rope

The tension in the rope is 10 N

Explanation:

The Force Vector

Like all vectors, the force has a magnitude and direction. Vectors can be decomposed into two perpendicular components on both axes.

The tension in the rope (F) can be calculated by using vector decomposition as follows.

The figure included below shows a force F which horizontal component is known to have a value of Fx= 5 Nw. The angle formed by the force and its horizontal component is 60°.

We can use the trigonometric ratio called the cosine to find the magnitude of F as follows:

Solving for F:

Thus, F = 10 N

The tension in the rope is 10 N

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  the grams     of oxygen gas   that can be produced     is 20.6   grams of o₂

calculation

2liclo₃ →   2 licl + 3 o₂

step 1:   find the moles of liclo₃

moles = mass÷ molar mass

from periodic table the molar mass of liclo₃ =6.9 +35.5   +(16 x3) =90.4 g/mol

moles=38.7 g÷90.4 g/mol=0.4281   moles

step 2:   use the   mole ratio   to calculate the moles of o2

from equation above, liclo₃: o₂   is 2: 3  

therefore the moles of   o₂=0.4281 moles x3/2 =0.6422   moles

step 3: find mass   of o₂

mass= moles x molar mass

from periodic table the   molar mass of   o₂ = 16 x2= 32 g/mol

mass=0.6422   moles   x   32 g/mol = 20.6 grams of o₂